No, the speed of a ball thrown from the top of the Earth does not increase the further it falls, assuming we are considering a free-falling object under the influence of gravity and neglecting air resistance.
When an object is in free fall, like a ball falling towards the Earth's surface, its speed will increase initially due to the acceleration of gravity. However, as the object falls, it eventually reaches a terminal velocity, which is the maximum speed it can attain during free fall when the gravitational force and air resistance balance each other.
For a ball falling from the top of the Earth, as it gains speed due to gravity, the air resistance acting on it also increases. Eventually, the air resistance becomes equal in magnitude to the gravitational force, causing the net force on the ball to become zero. At this point, the ball reaches its terminal velocity and its speed remains constant, without any further increase. The specific value of the terminal velocity depends on factors such as the shape and size of the object, as well as the density of the surrounding air.
Therefore, while the speed of a ball thrown from the top of the Earth increases initially, it eventually reaches a terminal velocity and does not continue to increase as it falls further.